Cohen–Hewitt factorization theorem

In mathematics, the Cohen–Hewitt factorization theorem states that if ${\displaystyle V}$ is a left module over a Banach algebra ${\displaystyle B}$ with a left approximate unit ${\displaystyle (u_{i})_{i\in I}}$, then an element ${\displaystyle v}$ of ${\displaystyle V}$ can be factorized as a product ${\displaystyle v=bw}$ (for some ${\displaystyle b\in B}$ and ${\displaystyle w\in V}$) whenever ${\displaystyle \displaystyle \lim _{i\in I}u_{i}v=v}$. The theorem was introduced by Paul Cohen (1959) and Edwin Hewitt (1964).

References

• Cohen, Paul J. (1959), "Factorization in group algebras", Duke Mathematical Journal, 26: 199–205, doi:10.1215/s0012-7094-59-02620-1, MR 0104982
• Hewitt, Edwin (1964), "The ranges of certain convolution operators", Mathematica Scandinavica, 15: 147–155, MR 0187016